ON THE FAMILY OF CUBIC PARABOLIC POLYNOMIALS

Author(s)

Alves, Alexandre ; Salarinoghabi, Mostafa

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. N/A, p. 14-pg., 2021-01-21.

Abstract

For a sequence (a(n)) of complex numbers we consider the cubic parabolic polynomials f(n)(z) = z(3) + a(n)z(2) + z and the sequence (F-n) of iterates F-n = f(n) circle...circle f(1). The Fatou set F-0 is the set of all z is an element of (C) over cap such that the sequence (F-n) is normal. The complement of the Fatou set is called the Julia set and denoted by J(0). The aim of this paper is to study some properties of J(0). As a particular case, when the sequence (a(n)) is constant, a(n) = a, then the iteration F-n becomes the classical iteration f(n) where f(z) = z(3) + az(2) + z. The connectedness locus, M, is the set of all a is an element of C such that the Julia set is connected. In this paper we investigate some symmetric properties of M as well. (AU)

• FAPESP's process: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision
• Grantee: Farid Tari
• Support Opportunities: Research Projects - Thematic Grants